Stars: Their Properties. T. K. Prasad http://www.cs.wright.edu/~tkprasad (Adapted from a lecture by Daniel Wang of UMass). Twinkle, twinkle, little star, How I wonder what you are. Up above the world so high, Like a diamond in the sky. Stars. Are Stars similar to our Sun?
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T. K. Prasad
(Adapted from a lecture by Daniel Wang of UMass)
Twinkle, twinkle, little star,How I wonder what you are.Up above the world so high,Like a diamond in the sky.
Are Stars similar to our Sun?
How far away are they?
Where did they come from?
What do they do?
Do they live forever?
To infer these parameters, we need to know the distance!
We can measure distances by comparing the position of objects observed from two ends of the “baseline” of a triangle.
If we lived on Mars, orbiting 1.5 times farther away from the Sun, the parallax would be
1 / 0.7 = 1.4 parsec
This is about 4.3 light years
or about 27,000,000,000,000 miles !
Suppose a star has a parallax of 0.01 arc seconds. How many parsecs away is it?
distance (in parsecs) = 1 / parallax (in arcsec)
Overall spectral shape (the peak of the blackbody continuous spectrum) is related to its temperature by
Wien’s Displacement Law:
T =2.9 × 106 K
More accurately, spectroscopically
Oh Be A Fine Girl/Guy, Kiss Me!
50,000 K 3,000 K
Other Mnemonics: e.g., Officially, Bill always felt guilty kissing Monica Lewinsky tenderly
Stellar Radii vary in sizefrom ~1500 RSun for a large Red Giant to 0.008 RSun for a WhiteDwarf.
How do we determine the radius of a star?
The angular radius of the Sun is about 103 arc seconds. If another star like the Sun was 5 parsecs away (about 106 AU), what would its angular radius be?
A star’s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law:
Two stars have the same surface temperature, butthe radius of one is 10 times the radius of the other.The larger star is
1) 10 times more luminous
2) 100 times more luminous
4) 1/10th as luminous
5) 1/100th as luminous
Suppose two stars are at equal distance and have the sameradius, but one has a temperature that is twice as great as theother. The apparent brightness of the hotter star is ____ as the other.
1) 1/2 as great
2) 1/4 as great
4) 4 times
5) 16 times as great
Distance + apparent brightness
( L=4D2 B)
Spectral type (or color)
Luminosity + temperature
Apparent brightness (B)
Luminosity and temperature are the two independent intrinsic parameters of stars.
Newton was able to derive Kepler’s Third Law from his own Law of Gravity. In its most general form:
P2 (mA + mB)= a3
The orbital period of two objects (P) depends on the distance between them (a) and the sum of the masses of both objects (mA + mB).
So if P and a can be measured, mA + mB can be estimated.
Each star in a binary system moves in its own orbit around the system's center of mass.
The primary importance of binaries is that they allow us to measure stellar parameters (especially mass).
We get the sum of the masses unless we see both stars moving.
But for most binaries, one cannot separate the stars even with most powerful telescopes. For them, we need to use the spectroscopic information.
Recall: Doppler Shift tells only if it is moving toward or away
From the eclipse duration, and orbital speed, we can also find the size of the star.
Thus one typically can tightly constrain the star masses in eclipsing binaries.
How may we classify stars?
We can take a census of stars and see what’s out there.
But first, let’s do some sociology in the classroom.
Make a plot that shows the generalrelationship between height and weight for humans.
- now add to your plot the population of basketball players who are very tall and very thin.
- now add the population of obese wrestlers
Around 1910, Ejnar Hertzsprung (Dane) and Henry Norris Russell (American) had the idea of plotting the luminosity of a star against its spectral type. For a star cluster, all the stars are at the same distance. So, apparent brightness vs spectral type is basically the same as luminosity vs temperature. They found that stars appeared only in certain parts of the diagram.
The Main Sequence
- Red Giant starsare very large, cooland quite bright.
e.g., Betelgeuse is150,000 times moreluminous than the Sunbut is only 3,500K onthe surface. It’s radiusis 1,000 times that of the Sun.
- White Dwarfsare hot, but sincethey are so small,they are not veryluminous.
1. MS, 2. H He, 3. M, 4. upperright, 5. lowerleft, 6. upperleft, 7. lowerright, 8. normally we don’t
rate of consumption
M3.5Mass-Lifetime Relation (MS)
O5 V (40Ms) : 1 Myr
G2 V (Sun) : 10 Gyr
M5 V (0.2 Ms) : 500 Gyr
e.g. for a 4 Msun star (e.g. Vega)
L = 43.5 = 128 Lsun
tlife = 4–2.5 = 0.03tsun = 300 Myr
We can date a cluster by observing itspopulation ofstars.
The oldest clustersknown have beenmeasured to be ~13 billion years old.
Anatomy of a Main Sequence Star
As hydrogen in the core is being used up, it starts to contract, raising temperature in the surrounding. Eventually, hydrogen will burn only in a shell. There is less gravity from above to balance this pressure. The Sun will then swell to enormous size and luminosity, and its surface temperature will drop, a red giant.
Sun in ~5 Gyr
The Sun will expand and cool again, becoming a red giant. Earth will be engulfed and vaporized within the Sun. The Sun’s core will consist mostly of carbon.
L = T4 4 R2
L = T4 4 R2. If Star A is twice as hot and one fourth the radius of Star B, then it should be…
(1) 1/4 as luminous as Star B
(2) just as luminous as Star B
(3) 16 times as luminous as Star B
(4) 64 times as luminous as Star B
(1) they are very rare and all very far away.
(2) they are so cool that they only emit in the infrared.
(3) they are too dim to be seen even if they are only a few light years away.